Effects of temperature on structure and mobility of the 〈1 0 0〉 edge dislocation in body-centred cubic iron

Dislocation segments with Burgers vector b = 〈1 0 0〉 are formed during deformation of body-centred-cubic (bcc) metals by the interaction between dislocations with b = 1/2〈1 1 1〉. Such segments are also created by reactions between dislocations and dislocation loops in irradiated bcc metals. The obstacle resistance produced by these segments on gliding dislocations is controlled by their mobility, which is determined in turn by the atomic structure of their cores. The core structure of a straight 〈1 0 0〉 edge dislocation is investigated here by atomic-scale computer simulation for α-iron using three different interatomic potentials. At low temperature the dislocation has a non-planar core consisting of two 1/2〈1 1 1〉 fractional dislocations with atomic disregistry spread on planes inclined to the main glide plane. Increasing temperature modifies this core structure and so reduces the critical applied shear stress for glide of the 〈1 0 0〉 dislocation. It is concluded that the response of the 〈1 0 0〉 edge dislocation to temperature or applied stress determines specific reaction pathways occurring between a moving dislocation and 1/2〈1 1 1〉 dislocation loops. The implications of this for plastic flow in unirradiated and irradiated ferritic materials are discussed and demonstrated by examples.     

Plastic deformation of wadsleyite: IV Dislocation core modelling based on the Peierls–Nabarro–Galerkin model

In this paper, we determine dislocation core structures and Peierls stresses of wadsleyite, a high-pressure mineral present in the Earth mantle. We use a Peierls–Nabarro model combined with a finite-element method in which we introduce two-dimensional generalized stacking fault energies. Several potential slip planes of wadsleyite are considered. The results show that dislocations in this mineral can exhibit complex dislocation cores with linear or non-collinear dissociation and even three-dimensional dislocation cores. The calculation of the Peierls stresses gives information on the potential activity of slip systems governing the plasticity of wadsleyite. Our study confirms experimental observations that ½〈1 1 1〉{1 0 1} is the easiest slip system in this structure at high-pressure and that [1 0 0](0 1 0) is the second easiest. Both these easily slip systems have dislocations that dissociate into collinear partial dislocations. In contrast [0 1 0] dislocations with very large Burgers vector (11.2 Å) are stabilized by complex dissociations involving four partial dislocations.     

Simulation of the interaction between an edge dislocation and a 〈1 0 0〉 interstitial dislocation loop in α-iron

Atomic-level simulations are used to investigate the interaction of an edge dislocation with 〈1 0 0〉 interstitial dislocation loops in α-iron at 300 K. Dislocation reactions are studied systematically for different loop positions and Burgers vector orientations, and results are compared for two different interatomic potentials. Reactions are wide-ranging and complex, but can be described in terms of conventional dislocation reactions in which Burgers vector is conserved. The fraction of interstitials left behind after dislocation breakaway varies from 25 to 100%. The nature of the reactions requiring high applied stress for breakaway is identified. The obstacle strengths of 〈1 0 0〉 loops, 1/2〈1 1 1〉 loops and voids containing the same number (169) of point defects are compared. 〈1 0 0〉 loops with Burgers vector parallel to the dislocation glide plane are slightly stronger than 〈1 0 0〉 and 1/2〈1 1 1〉 loops with inclined Burgers vector: voids are about 30% weaker than the stronger loops. However, small voids are stronger than small 1/2〈1 1 1〉 loops. The complexity of some reactions and the variety of obstacle strengths poses a challenge for the development of continuum models of dislocation behaviour in irradiated iron.     

Stress dependence of the Peierls barrier of 1/2〈1 1 1〉 screw dislocations in bcc metals

The recently formulated constrained nudged elastic band method with atomic relaxations (NEB + r) (Gröger R, Vitek V. Model Simul Mater Sci Eng 2012;20:035019) is used to investigate the dependence of the Peierls barrier of 1/2〈1 1 1〉 screw dislocations in body-centered cubic metals on non-glide stresses. These are the shear stresses parallel to the slip direction acting in the planes of the 〈1 1 1〉 zone different from the slip plane, and the shear stresses perpendicular to the slip direction. Both these shear stresses modify the structure of the dislocation core and thus alter both the Peierls barrier and the related Peierls stress. Understanding of this effect of loading is crucial for the development of mesoscopic models of thermally activated dislocation motion via formation and propagation of pairs of kinks. The Peierls stresses and related choices of the glide planes determined from the Peierls barriers agree with the results of molecular statics calculations (Gröger R, Bailey AG, Vitek V. Acta Mater 2008;56:5401), which demonstrates that the NEB + r method is a reliable tool for determining the variation in the Peierls barrier with the applied stress. However, such calculations are very time consuming, and it is shown here that an approximate approach of determining the stress dependence of the Peierls barrier (proposed in Gröger R, Vitek V. Acta Mater 2008;56:5426) can be used, combined with test calculations employing the NEB + r method.     

Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of 1/2〈1 1 1〉 screw dislocations at 0 K

Owing to their non-planar cores, 1/2〈1 1 1〉 screw dislocations govern the plastic deformation of body-centered cubic (bcc) metals. Atomistic studies of the glide of these dislocations at 0 K have been performed using Bond Order Potentials for molybdenum and tungsten that account for the mixed metallic and covalent bonding in transition metals. When applying pure shear stress in the slip direction significant twinning–antitwinning asymmetry is displayed for molybdenum but not for tungsten. However, for tensile/compressive loading the Schmid law breaks down in both metals, principally due to the effect of shear stresses perpendicular to the slip direction that alter the dislocation core. Recognition of this phenomenon forms a basis for the development of physically based yield criteria that capture the breakdown of the Schmid law in bcc metals. Moreover, dislocation glide may be preferred on {1 1 0} planes other than the most highly stressed one, which is reminiscent of the anomalous slip observed in many bcc metals.     

Tensile strength of 〈1 0 0〉 and 〈1 1 0〉 tilt bicrystal copper interfaces

Molecular dynamics (MD) simulations are used to model dislocation nucleation at or near symmetric tilt bicrystal copper interfaces with 〈1 0 0〉 or 〈1 1 0〉 misorientation axes. MD simulations indicate that orientation of the opposing lattice regions and the presence of certain structural units are two critical attributes of the interface structure that affect the stress required for dislocation nucleation. Boundaries that contain the E structural unit are found to emit dislocations at comparatively low tensile stress magnitudes. A simple model is proposed to illustrate the impact of interfacial porosity and stresses acting on the slip-plane in non-glide directions on tensile interface strength. Accounting for interfacial porosity through an average measure is found to be sufficient to model the tensile strength of boundaries with a 〈1 0 0〉 misorientation axis and many boundaries with a 〈1 1 0〉 misorientation axis.     

High-temperature strength and deformation of γ/γ′ two-phase Co–Al–W-base alloys

The high-temperature strength and deformation behavior of γ/γ′ two-phase Co–Al–W-base alloys have been studied with polycrystalline and single-crystal materials. The ternary, quaternary and higher-order alloys containing Ta, Cr and/or Re exhibit flow stress anomalies above 873 K due to slip of pairs of 1/2〈1 1 0〉 superpartial dislocations on {0 0 1} planes, in addition to {1 1 1} planes, in the γ′ precipitates. Compression tests on the single-crystal specimens reveal a true anomalous peak temperature of 1073 K for both ternary and Ta-containing quaternary alloys. Above the peak, the ternary alloy exhibits a rapid decrease in strength with temperature, as 1/2〈1 1 0〉 dislocations bypass the γ′ precipitates without significant shearing. Conversely, the Ta-containing quaternary alloy sustains strength to higher temperatures due to the activation of 1/3〈1 1 2〉 partial dislocation slip that introduces a high density of stacking faults in the γ′ precipitates.     

Determination of slip systems and their relation to the high ductility and fracture toughness of the B2 DyCu intermetallic compound

DyCu single crystals with CsCl-type B2 structure were tensile tested at room temperature. Slip trace analysis shows that the primary slip system in DyCu with a tensile axis orientation of 〈1 1 0〉 is {1 1 0}〈0 0 1〉 and the critical resolved shear stress for {1 1 0}〈0 0 1〉 slip is 18 MPa. Slip traces were also observed from a secondary slip system, {1 1 0}〈1 1 1〉, and this slip system appears to be a key contributor to the previously reported high ductility and high fracture toughness of polycrystalline DyCu. Transmission electron microscopy determinations of the Burgers vectors of dislocations in tensile tested specimens revealed 〈1 0 0〉 and 〈1 1 1〉 dislocations, with 〈1 0 0〉-type dislocations being more abundant. The implications of these findings for the understanding of the mechanical properties of DyCu and the large family of ductile rare earth B2 intermetallics are discussed.     

Observations of a〈0 1 0〉 dislocations during the high-temperature creep of Ni-based superalloy single crystals deformed along the [0 0 1] orientation

A NASAIR-100 superalloy single crystal was tested in tension creep at 1000 °C at a stress of 148 MPa, for a time period of 20 h and to a strain of 1.1%. Analysis of the resulting dislocation structures after rafting was completed reveals the frequent presence of all three types of a〈0 1 0〉 dislocations in the γ′ particles. Two of these families experience no resolved forces due to the applied stress. It is proposed that these a〈0 1 0〉 dislocations form as a result of the combination of two dissimilar a/2〈0 1 1〉 dislocations entering from γ channels. The possible driving forces for the movement of these a〈0 1 0〉 dislocations are discussed, and a novel recovery mechanism during creep of rafted microstructures is introduced on the basis of these observations.     

Atomistic study of edge and screw 〈c + a〉 dislocations in magnesium

The gamma surfaces in the pyramidal I {1 ?1 0 1} and II {1 1?2 2} planes for hexagonal close packed Mg have been calculated using two embedded-atom-method potentials and by ab initio methods, and reasonable agreement is obtained for key stacking fault energies. Screw and edge 〈c + a〉 dislocation core structures and Peierls stresses at 0 K and finite temperature have been examined using the embedded-atom-method potentials. Screw 〈c + a〉 dislocations glide in the {1 ?1 0 1} pyramidal plane I, and in the prism plane for larger stresses, but not in the {1 1 ?2 2} plane as observed in experiments. However, the preference for pyramidal I glide correlates well with the gamma surfaces. New low energy edge 〈c + a〉 dislocation cores were found in addition to the sessile Type I and Type III cores observed in previous simulations while the Type II core was not observed. The lowest energy core is a glissile core that lies in the {1 1 ?2 2} plane and has a 3 nm long {1 1 ?2 1} twin embryo, rather than the sessile Type III core found in previous simulations. As the temperature increases from 0 to 300 K, the Peierls stresses in compression/tension drop from ?80 MPa/+140 MPa and ?140 MPa/+220 MPa for the most glissile screw and edge dislocations to ?5/+2.5 MPa and ?27/+5 MPa, and dislocation glide changes from kink motion to face-centered-cubic-like motion. At 300 K and under an applied stress, almost all the edge cores found at low temperature transform into a glissile core denoted IT, which glides at low stresses. Thus, at 300 K both screw and edge 〈c + a〉 dislocations were found to glide at stresses smaller than the ～40 MPa measured experimentally.     

Deformation mechanisms in a Ru–Ni–Al ternary B2 intermetallic alloy

Deformation mechanisms in a B2 Al50Ni5Ru45 alloy have been studied in compression over the temperature range 298–1323 K. The alloy exhibited a low temperature sensitivity of the flow stress over the temperature range 298–973 K. The strain rate sensitivity below 973 K was relatively low, similar to binary RuAl-based alloys. Dislocation analyses after room temperature compression indicate the presence of 〈1 0 0〉 and 〈1 1 0〉 dislocations on {1 1 0} planes, with the 〈1 0 0〉 dislocations present with slightly higher densities. Compression creep tests at stress levels between 300 MPa and 500 MPa revealed exceptional creep strength in the temperature range investigated. The predominant dislocation substructure after creep deformation consisted of uniformly distributed, cusped 〈1 0 0〉-type screw dislocations on {1 1 0} planes. The deformation behavior and creep mechanisms are discussed in comparison with other high melting temperature B2 intermetallics.     

Mechanical properties and determination of slip systems of the B2 YZn intermetallic compound

Single crystal specimens of YZn (B2) were tested in tension at room temperature. Specimens with a [1 0 1] tensile axis orientation exhibited {0 1 1}〈1 0 0〉 primary slip and an ultimate tensile strength of 365 MPa at 3.7% elongation. Specimens with [0 0 1] and [1 1 1] tensile axis orientations showed no slip lines and fractured at a stress of 180 MPa at 3.3% and 130 MPa at 2.9% elongation, respectively. Transmission electron microscopy (TEM) examination of the Burger’s vector of dislocations in tensile tested specimens revealed 〈1 0 0〉-type dislocations. TEM analysis suggested that a secondary slip system, {0 0 1}〈1 0 0〉, may be active. Banded features with a {0 2 1} orientation were observed in deformed YZn; these may be slip traces produced by the cross-slip of 〈1 0 0〉 dislocations. Acting together, {0 1 1}〈1 0 0〉 and {0 0 1}〈1 0 0〉 slip provide only three independent slip systems, and no extra independent systems are provided by the cross-slip. This finding is consistent with the low ductility of YZn.     

Micromechanisms of fracture in NiAl studied by in situ straining experiments in an HVEM

The room temperature brittleness of NiAl constitutes a major problem for technical applications. In order to investigate the micromechanisms of fracture in NiAl, we have carried out in situ tensile straining experiments on stoichiometric NiAl single crystals in a high-voltage electron microscope. According to our observations, crack propagation always involves dislocation activity around the crack tip, even in the hard orientation at room temperature. The Burgers vectors and the typical arrangements of the dislocations, as well as the extension of the corresponding plastic zone vary with the loading direction and the orientation of the microcrack versus potential glide systems. We observe that local concentrations of slip leads to irregular deviation of the cleavage plane from the {1 1 0} facets one usually observes at the macroscopic level. The results of our experiments help to understand why the mode I fracture toughness of NiAl is significantly larger for 〈1 0 0〉 loading directions than for non-〈1 0 0〉 directions.     

Multiscale modeling of plastic deformation of molybdenum and tungsten. III. Effects of temperature and plastic strain rate

In this paper, we develop a link between the atomic-level modeling of the glide of 1/2〈1 1 1〉 screw dislocations at 0 K and the thermally activated motion of these dislocations via nucleation of pairs of kinks. For this purpose, we introduce the concept of a hypothetical Peierls barrier, which reproduces all the aspects of the dislocation glide at 0 K resulting from the complex response to non-glide stresses expressed in a compact form by the yield criteria advanced in Part II. To achieve this, the barrier is dependent not only on the crystal symmetry and interatomic bonding but also on the applied stress tensor. Standard models are then employed to evaluate the activation enthalpy of kink-pair formation, which is now also a function of the full applied stress tensor. The transition state theory then links this mechanism with the temperature and strain rate dependence of the yield stress.     

Mechanical properties and hardening mechanism of Fe–Al–Ni single crystals containing NiAl precipitates

The microstructures and mechanical properties of Fe–23.0 Al–6.0 Ni (at.%) single crystals containing NiAl precipitates were investigated and the hardening mechanism due to the precipitates was discussed, focusing on the activated slip systems. When these alloys were slowly cooled to room temperature after homogenization at 1373 K, the NiAl phase with the B2 structure precipitated in the body-centered cubic (bcc) Fe–Al matrix, satisfying the cube-on-cube relationship with a small misfit strain. The single crystals containing the NiAl precipitates exhibited a high yield stress above 1 GPa at room temperature. In addition, the activated slip system and deformation behavior depended strongly on the loading axis. For instance, 〈1 1 1〉 slip, which is the primary slip for the bcc matrix, occurred at 〈1 4 9〉 and 〈0 0 1〉 orientations and the NiAl precipitates were sheared by the slip. A critical resolved shear stress of 〈1 1 1〉 slip in the NiAl phase was known to be extremely high, which led to strong precipitation hardening. On the other hand, at 〈5 5 7〉 and 〈0 1 1〉 orientations, 〈0 0 1〉 slip, which is the primary slip system for the NiAl precipitates, forcibly sheared the bcc Fe–Al matrix, also leading to strong hardening. Thus, in the Fe–Al–Ni alloys, the difference in the primary slip system between the bcc Fe–Al matrix and the NiAl precipitates resulted in extreme hardening. This hardening mechanism caused by the NiAl precipitates effectively increased the yield stress even at high temperatures. In fact, the crystals exhibited a high yield stress at ～1 GPa up to 823 K.     

High temperature strengthening of the FeAl intermetallic phase-based alloy

The cause of the positive temperature dependence of the yield stress B2 FeAl alloys is still controversial. In the literature several models have been proposed but none of them fully accepted. In the present work results of studies of the yield stress, long range order parameter, magnetic susceptibility and structure versus temperature for the multi-component alloy on base of the B2 FeAl phase are presented.Results of TEM and HREM observations excluded precipitation hardening and the presence of antiphase domains as the reasons for the thermal hardening of the studied material. Detailed studies of the dislocation structure after small deformation of the alloy did not reveal the reaction of massive decomposition of the 〈1 1 1〉 superdislocation for the 〈1 0 0〉 and 〈0 1 1〉 in the temperature range of the anomaly occurrence.The plastic deformation process up to 1073 K proceeded by movement of the 〈1 1 1〉 type dislocations. For the first time a clear dependence of the yield stress temperature changes on the long range order parameter for the alloy on base of the B2 FeAl phase was obtained.     

Spatial characterisation of the orientation distributions in a stable plane strain-compressed Cu crystal: A statistical analysis

Single copper crystals of the stable Goss orientation {0 1 1}〈1 0 0〉 were deformed in plane strain compression and the deformation-induced dislocation structures were investigated by high-resolution electron backscattered diffraction. Although the orientation maps exhibited an anisotropic dislocation boundary structure it was shown that the mean disorientation angle between point pairs saturated and became isotropic if their spacing was large enough (typically >30 μm). This saturation behaviour was interpreted as being a consequence of the anti-correlations between nearby dislocation boundaries and is discussed in terms of recent stochastic models of boundary formation. It was found that the disorientation boundaries, which were considered as being formed at relatively low strains, underwent rigid body-like rotations during deformation.     

Contribution of non-octahedral slip to texture evolution of fcc polycrystals in simple shear

The contribution of non-octahedral {1 0 0}〈1 1 0〉 slip to texture evolution under simple shear in face-centred cubic (fcc) polycrystals was studied. It was found that, by adding the {1 0 0}〈1 1 0〉 slip system family to the usual {1 1 1}〈1 1 0〉, the ideal orientations remain the same. However, the stability of the ideal orientations, the rotation field and the rate of change of the orientation density function were affected by the non-octahedral slip activity. The stress state, the slip distribution and the form of the equipotential functions were also examined along the ideal fibres. Finally, the texture evolution in pure aluminium during equal channel angular extrusion was simulated and analysed.     

Microstructure and microtexture evolution during strain path changes of an initially stable Cu single crystal

The microstructure and microtexture evolution in a deformed Goss oriented crystal were characterized after a sample rotation and consequent change in strain path, over a range of scales by optical microscopy, high resolution scanning electron microscopy equipped with field emission gun and electron packscattered diffraction facilities and transmission electron microscopy orientation mapping. High purity copper single crystals with initial Goss{1 1 0}〈0 0 1〉 orientation were channel-die compressed 59% to develop a homogeneous structure composed of two sets of symmetrical primary microbands. New samples with ND rotated orientations of Goss{1 1 0}〈0 0 1〉, brass{1 1 0}〈1 1 2〉, M{1 1 0}〈1 1 1〉 and H{1 1 0}〈0 0 1〉, were then cut out and further compressed in channel-die by a few per cent. The change in flow stress could be correlated with the change in dislocation substructure and microtexture, particularly along shear bands initiated by the strain path change. In the H{1 1 0}〈0 1 1〉 and M{1 1 0}〈1 1 1〉 orientations, the flow stress increased by Taylor factor hardening then decreased by intense macroscopic shear band (MSB) formation. In the softer brass orientation and in the absence of Taylor factor hardening, more diffuse MSB formation occurred. The local rotations in the band were used to deduce the possible local slip systems initiated during the strain path change.     

Orientation- and microstructure-dependent deformation in metal nanowires under bending

Device miniaturization requires the bending of nanowires (NWs) on the nanoscale. To explore the mechanical behavior the mechanisms of plastic deformation of nickel nanowires of different orientations, sizes and twin structures under bending were investigated by means of molecular dynamics simulation. We show that plastic deformation can be either homogeneous or heterogeneous, depending on the NW orientation. Bending 〈1 2 1〉 oriented NW leads to homogeneous plastic flow, attributed to the large capacity for storage of axial extended dislocations (AEDs). AEDs are formed by constriction and cross-slip of inclined extended dislocations to the neutral (1 1 1) planes. The stacking of AEDs forms new defect structures, such as micro-twins and small hcp embryos. More localized deformation appears in NWs with 〈1 1 1〉 and 〈0 1 0〉 orientations at large bending angles, which is mainly caused by the pile-up and escape of inclined dislocations. The mechanical behavior of NWs is altered by introducing preset nano-twins,. The strength increases monotonically as the twin boundary spacing decreases. Among the three orientations the 〈1 2 1〉 oriented NWs with twin structure have been demonstrated to possess both high strength and ductility. A theoretical model based on geometrically necessary dislocations is proposed to quantify the contribution of various defects to the plastic deformation under bending, which links the continuum theory and atomistic simulations.